L-systems

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L-systems were originally introduced in the study of formal languages and were used as mathematical models of plant development. A deterministic L-system consists of an alphabet of letters, an initial word called the axiom, and a set of production rules that tell how to update the word from one iteration to the next. The graphical implementation of an L-system is based on turtle graphics, in which a point (the turtle) is given directions for moving around the plane. For example, in FractInt, the letter "F" is interpreted as a direction to move forward one step while drawing a line, and "+" is a command to turn counterclockwise 360/Angle degrees. More information about how to create an L-system with FractInt is available in FractInt's online help. The images below are thumbnails of higher resolution images that I created with FractInt. To view them in their full glory, follow these steps:
  1. Download FractInt
  2. Download marston.l, a text file containing the instructions for drawing the L-systems pictured below.
  3. Install FractInt and put marston.l in your FractInt directory.
  4. Run FractInt and choose the lsystem fractal type.
  5. Hit F6 to open marston.l.
Angle 12
Axiom -F++F[++F]--F[++F]--F[++F]--F[++F]--F[++F]--F
F=F[++F----F]--F++++F--F
Angle 8
Axiom F[+F[+F]--F]-F[-F]++F-F 
F=F[+F[+F]--F]-F[-F]++F-F
Angle 8
Axiom +F--F--F--F 
F=F[+F[+F]--F]-F[-F]++F-F
Angle 40
Axiom ++[F]++++++++[F]++++++++[F]++++++++[F]++++++++[F]
F=F[+++++F----------F]-----F++++++++++F-----F
Angle 40
Axiom ++[F]++++++++[F]++++++++[F]++++++++[F]++++++++[F]
F=F[+++++FF----------FF]-----FF++++++++++FF-----F
Brian Marston <webguy@fatdays.com>